Not unless you can whittle your fingernail into a #2 phillips head tip. Below is right out of the UL1363 standard:
3.1 MEANS FOR TEMPORARY MOUNTING – A mounting method that does not require the use of
tools for mounting or dismounting the RPT and conceals the head of a screw or other fastener so that it
cannot be tightened after the RPT is mounted.
(fyi, RPT stands for Relocatable Power Tap)

I don't even try to mount these things with screws any more. Double sided foam tape works very well and comes in types that are easy to remove or are very permanent depending on the need. Meeting all legal and use concerns is covered by using hook and loop material (Velcro) which is also available in varying strength. This is by definition "relocatable".

"Power strips really are suposed to be temporary...so if you need power somewhere all the time, Install some outlets!" I'd love to do that, and I agree it would be a better solution, but (in spite of having worked for years doing electrics elsewhere) I need papers to do anything like that in Australia, so I can't! I'm a comms guy and my boss won't pay for me to get sparky papers....

Power strips really are suposed to be temporary (like for meetings), so if you need power somewhere all the time, Install some outlets! (Or at least brew up a hardcore extension cord from some proper outlets and j-boxes from the hardare store)
That being said, one common annoyance that I found and repeatedly used a solution for *is* the mounting holes for things like power strips. For a good few devices they have screw holes put in a place where they are hard/impossible to measure/mark accurately. OPne example that comes to mind is a 'puck' GPS receiver that I mounted one time (I've done this with power strips as well). The holes were on the underside of the puck laid out in a *rough* circle. The trick is to take a peice of paper and do a pencil rubbing of the screw holes. Even if you flip the papaer over you can see the edges of the holes etched in to the paper and it makes it super easy to use a punch to transfer the hole centers into whatever you ahve to drill.

We have exactly the same problem in Australia. I once asked our supplier if he had any with the mounting lugs and he said (as TNW said above) that they are not meant to be mounted permanently. This is a pity as I use them under meeting room desks so users can plug in their laptops in meetings. You CAN (as Erickk said above) mount them fairly solidly if you get JUST the right size screws and get them JUST the right protrusion from the surface, but it's a pain....
I've had some success with 4 screws with large flat heads (We call them button heads here) using 2 on either long edge so that the heads overlap the adapter and hold it down to the surface. Makes for a good solid mount but there's probably a rule against it somewhere.
In Zimbabwe I used to get the ones with the British 3-pin square pin sockets. You could actually take them apart (shock, horror!) which I used to do to install VDRs for surge protection. But most of them did not have mounting lugs either.....

I believe the underlying problem is that both UL and the FTC are "paper tiger" agencies. I'm sure all the rules help lawyers get manufacturers off-the-hook when someone is hurt or killed - and that may be the main reason they exist. UL does a very poor job of educating users about hazards while the FTC looks the other way while unsafe products flood our markets. An example is the ubiquitous "3-to-2 prong" adapter. How many folks do you know that understand that these are to be used only in old facilities that have pre-1960 (2-prong) outlets *AND* that the clip or pigtail *MUST* be connected to the outlet cover screw (grounded via outlet saddle, metal J-box, and conduit back to neutral at the breaker panel)? Most folks believe they exist just as a matter of convenience or, worse yet, that they're intended to break those pesky ground loops. This use by the uninformed kills several people every year in the US (very often in sound systems where they've been installed to "eliminate hum". And then there are similar products, like the "Hum-X" that put a pair of back-to-back rectifiers in series with safety ground. Do you think a 5 A rectifier could be depended upon to carry 150 A fault current for 3 seconds (typical data from a UL study of fault currents and breaker trip times in 1,000 homes)? This device has been on the market for over 5 years and has no UL listing ... but our FTC has done nothing! It would probably alarm some folks to learn that "daisy-chaining" outlet strips is also a violation of National Electric Code.

It is quite easy to make an absolutely solid mounting of these plastic outlet strips, despite UL's intent to prevent this by mandating the use of keyhole slots.
Simply use optimally sized flat head screws. If you set the protrusion of the screw head just right, the conical rear surface of the screw head forms a sort of wedge against the keyhole slot as the slot is slid under the screw head. Get it just right, such that it takes a few taps with a small rubber mallet to seat the strip, and the strip gets powerfully wedged in place, assuming the screws are set into something solid.
As was pointed out above, the requirement to use keyholes is because UL and fire codes have long deemed cord connected outlet strips to be for temporary use only, so permanent mounting provisions (i.e. ears) are prohibited. Exceptions exist for hardwired strips, and for special purpose cord connected multiple outlets, such as for mounting on furniture, like AV equipment carts.

The reality is that, as has been mentioned, many of the power strips are indeed, JUNK. The reason for not having through-hole mounting is that some users would over-tighten the screws and crush the housing. So the solution is to simply not purchase the junk ones. The better ones are still available from companies like Newark, not as cheap, of course, but more durable. Also, companies like Tripp-Lite make a quite good ISOBAR unit that can have the mounting tabs exposed for mounting. My gripe is that all of the strips seem to have cords made with very stiff plastic material that is a pain to route.

The reason that most power strips do not have mounting ears anymore is because most of them are UL (or another NRTL) listed under UL Standard 1363 which is entitled "Relocatable Power Taps", the key word being "relocatable". The standard requires that the power strips NOT be capable of being permanently installed because they are supposed to be "relocatable" with out using any tools.